Solve for $x$ and $y$ using elimination. ${-2x-2y = -10}$ ${5x+2y = 19}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $3x = 9$ $\dfrac{3x}{{3}} = \dfrac{9}{{3}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-2x-2y = -10}\thinspace$ to find $y$ ${-2}{(3)}{ - 2y = -10}$ $-6-2y = -10$ $-6{+6} - 2y = -10{+6}$ $-2y = -4$ $\dfrac{-2y}{{-2}} = \dfrac{-4}{{-2}}$ ${y = 2}$ You can also plug ${x = 3}$ into $\thinspace {5x+2y = 19}\thinspace$ and get the same answer for $y$ : ${5}{(3)}{ + 2y = 19}$ ${y = 2}$